Axiomatizations and Computability of Weighted Monadic Second-Order Logic

Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted formulas output are evaluated. Gastin and Monmege (2018) gav...

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Vydáno v:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13
Hlavní autoři: Achilleos, Antonis, Pedersen, Mathias Ruggaard
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2021
Témata:
Automata
axiomatization
Complexity theory
Computer science
Model checking
monadic second-order logic
satisfiability
Semantics
Syntactics
weighted automata
weighted logic
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Abstract Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted formulas output are evaluated. Gastin and Monmege (2018) gave abstract semantics for a version of weighted monadic second-order logic to give a more general and modular proof of the equivalence of the logic with weighted automata. We focus on the abstract semantics of the logic and we give a complete axiomatization both for the full logic and for a fragment without general sum, thus giving a more fine-grained understanding of the logic. We discuss how common decision problems for logical languages can be adapted to the weighted setting, and show that many of these are decidable, though they inherit bad complexity from the underlying first- and second-order logics. However, we show that a weighted adaptation of satisfiability is undecidable for the logic when one uses the abstract interpretation.
AbstractList Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted formulas output are evaluated. Gastin and Monmege (2018) gave abstract semantics for a version of weighted monadic second-order logic to give a more general and modular proof of the equivalence of the logic with weighted automata. We focus on the abstract semantics of the logic and we give a complete axiomatization both for the full logic and for a fragment without general sum, thus giving a more fine-grained understanding of the logic. We discuss how common decision problems for logical languages can be adapted to the weighted setting, and show that many of these are decidable, though they inherit bad complexity from the underlying first- and second-order logics. However, we show that a weighted adaptation of satisfiability is undecidable for the logic when one uses the abstract interpretation.
Author Achilleos, Antonis
Pedersen, Mathias Ruggaard
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  givenname: Mathias Ruggaard
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  fullname: Pedersen, Mathias Ruggaard
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  organization: Reykjavik University,Department of Computer Science,Reykjavik,Iceland
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Snippet Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its...
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SubjectTerms Automata
axiomatization
Complexity theory
Computer science
Model checking
monadic second-order logic
satisfiability
Semantics
Syntactics
weighted automata
weighted logic
Title Axiomatizations and Computability of Weighted Monadic Second-Order Logic
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